Question 15 Marks
Using Euler's formula find the unknown:
|
Faces
|
?
|
5
|
20
|
|
Vertices
|
6
|
?
|
12
|
|
Edges
|
12
|
9
|
?
|
Answer
View full question & answer→We know that the Euler's formula is: F + V = E + 2
F + 6 = 12 + 2
F + 6 = 14
F = 14 - 6
F = 8
So, the number of faces in this polyhedron is 8.
We have to find the number of vertices.
Putting these values in Euler's formula:
5 + V = 9+ 25 + V = 11
V = 11 - 5
V = 6
So, the number of vertices in this polyhedron is 6.
Using Euler's formula:
20 + 12 = E + 2
32 = E + 2
E + 2 = 32
E = 32 - 2
E = 30
So, the number of edges in this polyhedron is 30.
- The number of vertices V is 6 and the number of edges E is 12.
F + 6 = 12 + 2
F + 6 = 14
F = 14 - 6
F = 8
So, the number of faces in this polyhedron is 8.
- Faces, F = 5
We have to find the number of vertices.
Putting these values in Euler's formula:
5 + V = 9+ 25 + V = 11
V = 11 - 5
V = 6
So, the number of vertices in this polyhedron is 6.
- Number of faces F = 20
Using Euler's formula:
20 + 12 = E + 2
32 = E + 2
E + 2 = 32
E = 32 - 2
E = 30
So, the number of edges in this polyhedron is 30.